Question

What are the critical values, if any, of `f(x)= sin^2x +cos^2x in [0,oo]`?

Answer 1

I'd say that every number in `[0,oo)` is a critical value.

Explanation:

`f(x) = sin^2x+cos^2x = 1`

So `f'(x) = 0`

The critical values of `f` are the numbers in the domain of `f` at which the derivative either does not exist or the derivative is `0`. Since the derivative is `0` for all numbers in the domain, I would say that every number in the domain is a critical value.